Solve for $x$ and $y$ using elimination. ${2x-3y = -14}$ ${-2x+2y = 8}$
Answer: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the equations together. Notice that the terms $2x$ and $-2x$ cancel out. $-y = -6$ $\dfrac{-y}{{-1}} = \dfrac{-6}{{-1}}$ ${y = 6}$ Now that you know ${y = 6}$ , plug it back into $\thinspace {2x-3y = -14}\thinspace$ to find $x$ ${2x - 3}{(6)}{= -14}$ $2x-18 = -14$ $2x-18{+18} = -14{+18}$ $2x = 4$ $\dfrac{2x}{{2}} = \dfrac{4}{{2}}$ ${x = 2}$ You can also plug ${y = 6}$ into $\thinspace {-2x+2y = 8}\thinspace$ and get the same answer for $x$ : ${-2x + 2}{(6)}{= 8}$ ${x = 2}$